Data.Fixed (original) (raw)

Recall that, for numeric types, [succ](Prelude.html#v:succ "Prelude") and [pred](Prelude.html#v:pred "Prelude") typically add and subtract1, respectively. This is not true in the case of [Fixed](Data-Fixed.html#t:Fixed "Data.Fixed"), whose successor and predecessor functions intuitively return the "next" and "previous" values in the enumeration. The results of these functions thus depend on the resolution of the [Fixed](Data-Fixed.html#t:Fixed "Data.Fixed") value. For example, when enumerating values of resolution 10^-3 of type Milli = Fixed E3,

succ (0.000 :: Milli) == 1.001

and likewise

pred (0.000 :: Milli) == -0.001

In other words, [succ](Prelude.html#v:succ "Prelude") and [pred](Prelude.html#v:pred "Prelude") increment and decrement a fixed-precision value by the least amount such that the value's resolution is unchanged. For example, 10^-12 is the smallest (positive) amount that can be added to a value of type Pico = Fixed E12 without changing its resolution, and so

succ (0.000000000000 :: Pico) == 0.000000000001

and similarly

pred (0.000000000000 :: Pico) == -0.000000000001

This is worth bearing in mind when defining [Fixed](Data-Fixed.html#t:Fixed "Data.Fixed") arithmetic sequences. In particular, you may be forgiven for thinking the sequence

[1..10] :: [Pico]

evaluates to [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] :: [Pico].

However, this is not true. On the contrary, similarly to the above implementations of [succ](Prelude.html#v:succ "Prelude") and [pred](Prelude.html#v:pred "Prelude"), enumFromTo :: Pico -> Pico -> [Pico] has a "step size" of 10^-12. Hence, the list [1..10] :: [Pico] has the form

[1.000000000000, 1.00000000001, 1.00000000002, ..., 10.000000000000]

and contains 9 * 10^12 + 1 values.

Since: base-2.1